All the Turbos are the same. Front, back, 1st gen or 2nd gen. The only difference is the wastegate for the front or rear turbo, which can be changed if you needed. All that 1st gen 2nd gen stuff is really irrelevant to anything except the front intake pipe and the ypipe the rubber intake pipe connects to.
I never understood what the big deal about the '2nd gen' hose was anyway. The turbos get smokey either way or they won't. I haven't seen anything showing 1Js using the longer hose to blow turbos significantly less than the short hose.
http://www.supraforums.com/forum/showthread.php?t=143293
This is the thread where it started but I never really bought into it. The only important thing that I picked up from it is to get a new PCV valve regardless if you have the 1st or 2nd.
I know this is a little over the top of what you asked but since you brought up 1st and 2nd gen 1Js, I thought I'd throw it in there...